### Abstract

Risk, or the probability of loss, depends on the amount of information available to predict outcomes, as well as the essentially random characteristics of the process. Probabilities calculated by traditional methods do not reflect information content directly. Therefore, traditional probabilities must be reported along with confidence intervals, particularly in situations in which information is limited. Interpretation of risk - expressed as a degree of confidence in a probability of some loss - is difficult. In this paper, information theory was used to estimate conditional probability distributions, representing risks, for which no data were available but one or two statistics (such as mean values) were known. The resulting distributions expressed information content directly. Revision of these distributions with additional information resulted in narrower distributions, in contrast with traditional approaches. Probabilities of cadmium removal efficiencies experienced for various durations were estimated from knowledge of total annual flow and residue. The complete particle-size distribution for a sand filter bed was predicted satisfactorily from knowledge of clear water headloss, verifying the method, and providing the basis for a rapid quality-control test for particle-size separators.

Original language | English |
---|---|

Pages (from-to) | 890-904 |

Number of pages | 15 |

Journal | Journal of Environmental Engineering |

Volume | 118 |

Issue number | 6 |

State | Published - Nov 1 1992 |

### Fingerprint

### ASJC Scopus subject areas

- Civil and Structural Engineering
- Environmental Science(all)
- Environmental Chemistry
- Environmental Engineering

### Cite this

*Journal of Environmental Engineering*,

*118*(6), 890-904.

**Information theory in risk analysis.** / Englehardt, James Douglas; Lund, J. R.

Research output: Contribution to journal › Article

*Journal of Environmental Engineering*, vol. 118, no. 6, pp. 890-904.

}

TY - JOUR

T1 - Information theory in risk analysis

AU - Englehardt, James Douglas

AU - Lund, J. R.

PY - 1992/11/1

Y1 - 1992/11/1

N2 - Risk, or the probability of loss, depends on the amount of information available to predict outcomes, as well as the essentially random characteristics of the process. Probabilities calculated by traditional methods do not reflect information content directly. Therefore, traditional probabilities must be reported along with confidence intervals, particularly in situations in which information is limited. Interpretation of risk - expressed as a degree of confidence in a probability of some loss - is difficult. In this paper, information theory was used to estimate conditional probability distributions, representing risks, for which no data were available but one or two statistics (such as mean values) were known. The resulting distributions expressed information content directly. Revision of these distributions with additional information resulted in narrower distributions, in contrast with traditional approaches. Probabilities of cadmium removal efficiencies experienced for various durations were estimated from knowledge of total annual flow and residue. The complete particle-size distribution for a sand filter bed was predicted satisfactorily from knowledge of clear water headloss, verifying the method, and providing the basis for a rapid quality-control test for particle-size separators.

AB - Risk, or the probability of loss, depends on the amount of information available to predict outcomes, as well as the essentially random characteristics of the process. Probabilities calculated by traditional methods do not reflect information content directly. Therefore, traditional probabilities must be reported along with confidence intervals, particularly in situations in which information is limited. Interpretation of risk - expressed as a degree of confidence in a probability of some loss - is difficult. In this paper, information theory was used to estimate conditional probability distributions, representing risks, for which no data were available but one or two statistics (such as mean values) were known. The resulting distributions expressed information content directly. Revision of these distributions with additional information resulted in narrower distributions, in contrast with traditional approaches. Probabilities of cadmium removal efficiencies experienced for various durations were estimated from knowledge of total annual flow and residue. The complete particle-size distribution for a sand filter bed was predicted satisfactorily from knowledge of clear water headloss, verifying the method, and providing the basis for a rapid quality-control test for particle-size separators.

UR - http://www.scopus.com/inward/record.url?scp=0026947269&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0026947269&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0026947269

VL - 118

SP - 890

EP - 904

JO - Journal of Environmental Engineering, ASCE

JF - Journal of Environmental Engineering, ASCE

SN - 0733-9372

IS - 6

ER -